We give necessary and sufficient conditions under which the reproducing kernel of a Pontryagin space of d×1 vector polynomials is determined by a generalized Nevanlinna pair of d×d matrix polynomials.
Linear Algebra and its Applications
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Ćurgus, Branko and Dijksma, Aad, "On the Reproducing Kernel of a Pontryagin Space of Vector Valued Polynomials" (2012). Mathematics. Paper 64.